Consider the cartesian product H=Z_2 X Z_n (as a set).Define a binary operation on H to be (i,j)*(k,l)=(i+k,(-1)^k *j+l), where i,j,k and l are vectors.
Show that H is a group under this operation, determine its order.
Let G = < a,b|a^n=1, b^2=1, abab^-1=1 >
Show that |G|<=2n.
Show that H is isomorphic to G.
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This provides an example of proving something is a group and that it is isomorphic.